Accuracy of prediction methods for sound transmission loss

The 33rd International Congress and Exposition
on Noise Control Engineering
Accuracy of Prediction Methods for
Sound Transmission Loss
K. O. Ballagh
Marshall Day Acoustics Ltd, P O Box 5811
Auckland 1036, New Zealand
[email protected]
Abstract [586] There are various methods for predicting the sound transmission loss of walls and
floors that can be used by noise control engineers. It is important to know how accurate these methods
are for typical constructions used in Building Acoustics. Results are presented for a number of
different constructions showing how accurately the results of predictions match experimental
laboratory results. The results will show the accuracy over the frequency range 50 to 5,000 Hz. Both
single and double partitions will be discussed.
1 INTRODUCTION
It is important to know the sound transmission loss of walls and floors in order to be able to
compare different constructions, to calculate acoustic privacy between apartments or noise levels
from outdoor sources such as road traffic, and to engineer optimum solutions to noise control
problems. Laboratory measurements have been made for many different types of partitions, but it is
impractical to test every possible design and so it is necessary to have reliable methods for
predicting the sound transmission loss of typical building constructions.
This paper presents a comparison of experimental measurements of the sound transmission of walls
and floors with theoretical models. Single homogeneous panels are examined first, with mass,
stiffness, damping and panel size found to be adequate to describe most common building
constructions. Double panel walls are then examined, with additional factors of airgap between the
panels, connections between the panels and acoustic absorption in the cavity enabling good
engineering predictions of sound transmission loss.
2 PREDICTION MODELS
2.1 Homogeneous Panels
For simple homogeneous panels the most important property is the mass per unit area of the panel,
and the well-known mass law [1] gives a very simple prediction of the transmission loss R.
R = 20 log(mf ) − 47
1/1
(1)
However, for most practical building materials the static stiffness must be sufficiently high that
coincidence between airborne and structure borne waves will occur within the frequency range of
interest (50 – 5,000 Hz). This was investigated by Cremer [2] and the mass law modified to include
the change in transmission at the critical frequency and above.
R = 20 log(mf ) − 10 log(2ηω / πωc) − 47
(2)
For most thin homogeneous materials commonly used in building construction this provides an
excellent prediction of the transmission loss over most of the frequency range. However, one
additional effect must be taken into account to obtain good accuracy at low frequencies. For typical
test construction of 10 – 12 m2 the radiation efficiency of forced waves must be taken into account
for frequencies of less than 200Hz. Sewell [3] gives the correction to the infinite area panel as
∆R = − log10 [ln(kA1 / 2 )] + 20 log10 [1 − (ω / ω c ) 2 ]
(3)
The simple expressions (1), (2) and (3) however, are not adequate to describe very thick and heavy
panels such as concrete or brick. For these types of panel shear waves become the dominant
flexural waves at high frequencies. This affects the transmission loss at high frequencies reducing
the frequency dependence to 6 dB/octave at high frequencies [4] instead of the 12dB/octave
behaviour of thin panels above the critical frequency.
2.2 Double Panels
Predicting the acoustic performance of double panels is often necessary. Many walls and floors are
constructed of thin linings with an airspace between, and these can, if correctly designed, give high
sound transmission loss. The simplest case to analyse is a partition consisting of two thin
homogeneous panels, separated by an airgap containing an acoustically absorbing blanket, and with
no interconnections between the two panels. Sharp [5] has developed expressions for the
transmission loss in 3 frequency ranges as follows:
R = 20 log( f (m1 + m2 )) − 47
R = R1 + R2 + 20 log( fd ) − 29
R = R1 + R2 + 6
f < f0
(4)
f 0 < f < f l (5)
f > fl
(6)
Where m1 and m2 are the surface masses of each panel and d is the depth of the airspace between, fo
is the mass-air-mass resonance frequency and fl is equal to (55/d) Hz. R1 and R2 are the transmission
losses for the individual panels calculated from (2).
These expressions do not contain any parameters to describe the variation in performance due to
different acoustic absorbers in the airspace and it is a practical problem of some interest to
determine this effect. Fahy [1] gives an alternative high frequency solution.
R = R1 + R2 + 8.6αd + 20 log10 ( β / k )
f > fl
where α and β are the real and imaginary parts of the propagation coefficient of the absorptive
blanket and k is the wave number.
2/2
(7)
2.3 Double Panels with Connections
While some constructions can approach the ideal of double panels without interconnections, in
practice most construction will have some type of solid or resilient connection between the panels.
Sharp [5] has developed relatively simple expressions for the transmission loss of double panels
with either point or line interconnections.
R = R1+ 2 + 20 log(e. f c ) + 20 log[m1 /(m1 + m2 )] − 45
R = R1+ 2 + 10 log(b. f c ) + 20 log[m1 /(m1 + m2 )] − 18
(8)
(9)
Where e and b are the spacing between the point and line connections respectively. These
expressions are correct only below the critical frequencies of both panels. Using Statistical Energy
Analysis expressions can be derived for the frequency range above the critical frequency of both
panels [6]. For interconnections that are not rigid, for instance resilient steel rails, or thin steel studs
Rindel has derived expressions that take account of the compliance of the connection [6] (see
reference for definition of the symbols).
8c 2
2c
R = R1+ 2 − 10 log[ 3 2 N p γ pκ p +
( Ll γ l κ l + 12 Lr γ r κ r )]
(10)
Sπf cl
Sπ f cp
3 COMPARISON BETWEEN THEORY AND RESULTS
3.1 Single Homogeneous Panels
In fig. 1 a comparison is made between 19 mm thick gypsum sheets fixed to one side of a frame
consisting of 100x50 mm timber studs at 600 mm centres. The total area of the panel is 10.8 m2
and mass per unit area of the gypsum board is 14.2 kg/m2. It can be seen that the agreement
between theory and measurement is excellent for most engineering purposes. However if the effect
of the radiation efficiency of a finite panel is not taken into account then the agreement at low
frequencies is not so good.
Sound Transmission Loss [dB]
60
50
40
30
20
10
0
50
100
200
400
800
1600
3150
frequency [Hz]
Fig. 1 Sound Insulation of 19mm thick gypsum board( - - - predicted for infinite panel,––– predicted for
finite panel allowing for radiation efficiency, * measured)
3/3
In fig 2, a comparison is made between the measured results for a 190mm thick concrete block wall
and the predictions of the mass law with allowance made for the effect of shear waves. It can be
seen that while agreement is not perfect above 1000 Hz that the theory with shear waves provides a
better prediction than the simple theory of Cremer.
Sound Transmission Loss [dB]
80
70
60
50
40
30
20
10
0
50
100
200
400
800
1600
3150
frequency [Hz]
Fig. 2 Sound insulation of 190mm thick concrete block wall
( – – –predicted with no shear waves, ––– predicted with shear waves, * measured)
3.2 Ideal Double Panels
Timber or steel framed walls that use two rows of independent studs can be modeled as ideal double
panel walls provided that as in a laboratory test, there is no significant flanking. The data in fig 3
shows a separate timber stud wall with two layers of 13mm thick fire rated gypsum board each side,
and with a 75mm thick fiberglass blanket of flow resistivity 1800 Rayls/m in the wall cavity. The
general agreement is good over the whole frequency range. In fig 4 a double stud wall is shown
that has a much thicker and denser absorbing blanket (160mm thick mineral wood with flow
resistivity of 25,000 Rayls/m). The measurement results show that adding the additional
propagation losses in the acoustic blanket improves agreement between theory and measurement.
Sound Transmission Loss [dB]
80
70
60
50
40
30
20
10
0
50
100
200
400
800
1600
3150
frequency [Hz]
Fig. 3: Sound insulation of double stud wall consisting of 1 layer of 13mm fire rated gypsum board each side
of 90mm steel studs with a 100mm thick polyester blanket in the cavity, total airspace 224mm
(––– predicted, * measured)
4/4
Sound Transmission Loss [dB]
90
80
70
60
50
40
30
20
10
0
50
100
200
400
800
1600
3150
frequency [Hz]
Fig. 4: Sound insulation of double stud wall consisting of 2 layers of 13mm gypsum board each side of 90mm
steel studs with a 2 layers of 80mm thick mineral wool blanket in the cavity, total airspace 260mm (- - predicted by expressions 4-6, ––– predicted with propagation losses in blanket, * measured)
3.3 Double Panels with Interconnections
A simple timber framed wall can be modeled with good accuracy as two panels with line
connections between them. This is demonstrated in fig 5, which shows good agreement over the
frequency range.
Sound Transmission Loss [dB]
80
70
60
50
40
30
20
10
0
50
100
200
400
800
1600
3150
frequency [Hz]
Fig. 5: Sound insulation of timber stud wall consisting of 1 layer of 10mm gypsum board screwed to one side
of 90mm studs with 2 layers of 10mm gypsum board screwed to the other side, with a 75mm fibreglass
blanket in the cavity (––– predicted, * measured)
5/5
Another common situation is a masonry wall with an attached lining. In this case expressions (4),
(5), and (6) are not applicable because the critical frequency of the masonry wall is low. In fig 6 the
agreement between theory using the modified SEA expression [6] and measurement is shown.
Sound Transmission Loss [dB]
80
70
60
50
40
30
20
10
0
50
100
200
400
800
1600
3150
frequency [Hz]
Fig. 6: Sound insulation of 190mm concrete block wall with 16mm gypsum board fixed to 40mm timber
battens fixed to wall, with a 38mm fibreglass blanket in the cavity (––– predicted, * measured)
The effect of resilient interconnections can be modeled with good accuracy using expressions (4),
(5), and (6) modified to account for the compliance of the interconnections. The comparison
between measurement and prediction is shown in figs 7 and 8.
Sound Transmission Loss [dB]
80
70
60
50
40
30
20
10
0
50
100
200
400
800
1600
3150
frequency [Hz]
Fig. 7: Sound insulation of steel stud wall consisting of 1 layer of 10mm gypsum board screwed to each side
of 64mm studs, with a 75mm fibreglass blanket in the cavity (––– predicted, * measured)
6/6
Sound Transmission Loss [dB]
80
70
60
50
40
30
20
10
0
50
100
200
400
800
1600
3150
frequency [Hz]
Fig. 8: Sound insulation of timber stud wall with a neoprene resilient isolators fixed to one side of the studs
with 2 layers of 13mm gypsum board fixed to each side, with a 75mm fibreglass blanket in the cavity
(––– predicted, * measured)
3.4 Overall Accuracy
The agreement shown in the figs above is generally very good, but his is a very limited set of
comparisons. In order to quantify the accuracy over a wide range of constructions a large number
of comparisons were made between theory and measurements. National Research Council (NRC)
in Canada has published measurements on more than 240 walls and floors [7,8]. Predictions were
made for each construction using the published properties of the materials and the descriptions of
the constructions. The mean difference in STC/Rw between measurement and theory was less than
0.5 dB and 90% of results were found to lie within ± 2.5 dB.
Sound Transmission Loss [dB]
20
15
10
5
0
-5
-10
-15
-20
50
100
200
400
800
1600
3150
frequency [Hz]
Fig. 9: Measured less predicted for 132 floors from ref [8] (– – – 10% and 90% limits, –––median error)
This is acceptable accuracy given that measurement repeatability and reproducibility between
laboratories is probably no better than ± 1.5-2 dB. The difference between theory and measurement
as a function of frequency is shown in Figure 9 and 10. It can be seen that the variations are
smallest at low frequency and tend to increase with frequency. The floors have only a small median
7/7
error over the whole frequency range while the models for walls tends to under predict by about 5
dB at mid frequencies.
Sound Transmission Loss [dB]
20.0
15.0
10.0
5.0
0.0
-5.0
-10.0
-15.0
-20.0
50
100
200
400
800
1600
3150
frequency [Hz]
Fig. 10: Measured less predicted for 112 walls from ref [7] (– – – 10% and 90% limits, –––median error)
4 CONCLUSIONS
The sound insulation of typical building constructions using either masonry or lightweight cavity
construction can be predicted with acceptable engineering accuracy over the frequency range
50-5,000 Hz using simple and readily available expressions.
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
F.Fahy, Sound and Structural Vibration Radiation, Transmission and Response, Academic Press, London, 1985.
L. Cremer, “Theorie der Schälldammung dünner Wände bei Schrägen einfall”, Akust. Ztg, 7, pp81 (1942).
E.C Sewell, “Transmission of reverberant sound through a single leaf partition surrounded by an infinite rigid
baffle”, Journal of Sound and Vibration 12 pp 21-32 (1970).
J.H. Rindel, “Sound Radiation from Building Structures and Acoustical Properties of Thick Plates”, COMETTSAVOIR Course, Noise Control in Buildings – Up-to-date Practice, CSTB, Grenoble, France (1995), pp 7-8.
B.H. Sharp, “Prediction Methods for the Sound Transmission of Building Elements, Noise Control Engineering
11, pp 63 – 63, (1978).
J. Kristensen & J.H. Rindel: "Bygningsakustik. Teori og praksis". SBI-anvisning 166, Statens
Byggeforskningsinstitut, SBI, Hørsholm 1989. (Translation to English available from JHR).
R.E. Halliwell, T.R.T. Nightingale, A.C.C. Warnock and J.A. Birta “Gypsum Board Walls: Transmission Loss
data”. National Research Council of Canada, Internal Report No. 761 (1998).
A.C.C. Warnock & J.A. Birta “Detailed Report for Consortium on Fire Resistance and Sound Insulation of
Floors: Sound Transmission and Impact Insulation Data in 1/3 Octave Bands”. National Research Council of
Canada, Internal Report No. 811 (2000).
8/8